Check this registry key to ensure ORACLE_HOME is configured for the service:
HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\ORACLE\KEY_XE\ORACLE_HOME
If that doesn't exist, check here:
HKEY_LOCAL_MACHINE\SOFTWARE\ORACLE\KEY_XE\ORACLE_HOME
Also make sure this other key is isn't pointing to your old client registry key:
HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\ORACLE\KEY_XE\ORACLE_HOME_KEY
or
HKEY_LOCAL_MACHINE\SOFTWARE\ORACLE\KEY_XE\ORACLE_HOME_KEY